Democratic Senate candidate Elizabeth Warren speaks with garage owner Jim Rousseau about one of his antique trucks following Warren's visit to a sewage treatment project on her "Build It Now" tour encouraging infrastructure spending.

The cloud stirred up by a group’s effort to increase voter registration among Massachusetts welfare recipients dovetails with the Democrats’ primary plan for winning this fall’s US Senate race, even if that effort is not sanctioned by the Patrick administration or state Democratic party.

That plan is this: increase turnout among traditional liberal Democratic constituencies by all means possible, swamping Senator Scott Brown and the Republican Party during a presidential year.

Senator Scott Brown

Steven Senne/AP

Brown’s rival, Harvard Law School professor Elizabeth Warren, is doing her part with tough talk about Wall Street, as well as policy proposals including an infrastructure plan aimed at winning votes from lunchbucket Democrats such as labor unions.

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The Massachusetts Democratic Party is doing its part with an aggressive effort to expand upon and invigorate the grassroots organization that propelled Deval Patrick to two terms as governor after 16 consecutive years of GOP control over the Corner Office.

And now Brown and the Massachusetts Republican Party are charging that Patrick’s administration itself, as well as an outside group guided by Warren’s own daughter, are trying to do their part by spending public funds to increase turnout among welfare recipients.

That’s the kind of downtrodden constituency that usually leans toward the Democrats and their belief in a strong social safety net.

The challenge to all that is that by tacking hard to the left, Warren and her party risk alienating unenrolled voters. At 52 percent of all registered voters, they represent the majority of the Massachusetts electorate.

Brown has been making a strong pitch for those voters with his heavy talk of and campaign commercials touting his bipartisan acts and Democratic supporters.

Never mind that such outreach is compelled by the National Voter Registration Act of 1993, also known as the “motor voter” law that has already made registration commonplace at the Registry of Motor Vehicles.

Nevermind, too, that the Republican Bush administration pushed for compliance with the act, or that Demos has worked with 18 states since 2004 to ensure they provide the voter registration compelled by it.

Nevermind, also, that the new outreach effort in Massachusetts—which includes spending $276,000 to mail voter registration forms to welfare recipients who should have received them when they visited DTA offices in person—is compelled by a settlement to the lawsuit filed by Demos and likeminded allies.

Brown has focused on the fact that Warren’s daughter, Amelia Warren Tyagi, is chairman of the board of New York-based Demos, and that the current state administration is Democratic.

The connection, in Brown’s mind, is that the state is spending public resources—with the figleaf of a lawsuit filed by what is ostensibly a pro-Warren group—in an effort to boost Warren’s campaign against him.

“I want every legal vote to count, but it’s outrageous to use taxpayer dollars to register welfare recipients as part of a special effort to boost one political party over another,” the senator said in a statement on Wednesday. “This effort to sign up welfare recipients is being aided by Elizabeth Warren’s daughter, and it’s clearly designed to benefit her mother’s political campaign.”

Then, in a line aimed at perpetuating the notion that Democrats and their allies are ganged up against him, Brown added: “It means that I’m going to have to work that much harder to get out my pro-jobs, pro-free enterprise message.”

Beyond marketing Brown’s hard knocks life story, one of his campaign’s principal aims has been to cast him as the underdog—the Republican David against the Democratic Goliath.

It’s a notion he stoked during his 2010 special election victory speech, when he proclaimed to the Schilling-embracing, Flutie-loving coalition that helped him defeat Democrat Martha Coakley, “I thought it was going to be me against the machine. I was wrong. It’s all of us against the machine. You have shown everyone now that you are the machine.”

Yet beyond the sympathy it evokes, the Democrats have approached his reelection campaign in a way that buttresses the sentiment.

Party Chairman John Walsh, who ran Patrick’s victorious 2006 gubernatorial campaign, said a party that had grown complacent after winning the Corner Office would rebound from its loss to Brown in 2010 with heavier turnout in 2012—a presidential election year.

Official returns showed that Brown received 1.168 million votes in the special election to replace the late Senator Edward M. Kennedy, or 52 percent of the total cast. Coakley got 1.059 million, or 47 percent.

A total of 2.249 million votes were cast, with Brown getting 109,000 more than Coakley.

Obama got 1.904 million votes, while McCain got 1.109 million. A total of 3.103 million votes were cast—or 854,000 more votes than in the Brown-Coakley special election. Brown received only 60,000 more votes than McCain, even when his special election was the lone contest on the ballot.

Democrats believe if there are similar turnout trends this fall, the extra voters will break proportionally for their Senate candidate.

That has been the guiding principle for the party’s 2012 Senate campaign.

She was encouraged by Washington Democrats including Harry Reid, who believed a victory by her over Brown would help ensure he remained as Senate majority leader.

She was boosted by pro-Democratic groups like EMILY’s List, which pledged to raise money for her campaign.

And her candidacy was sealed by support from Walsh himself, who appeared to abandon his proclamation of neutrality when he told the Globe last July, “I would love it if she were interested in joining the race.”

A couple weeks later, Warren did so.

Warren immediately made a splash with a video that went viral. It featured her addressing a group of supporters in Andover with her now-famous declaration: “There is nobody in this country who got rich on his own.”

In the ensuing months, Warren has worked hard to cultivate the Democratic garden.

Her schedule has been heavy with appearances before Democratic town committees, a common practice among first-time candidates like her who have to meet activists. She also worked party caucuses and the Democratic State Convention to avoid having a primary against fellow Democrats such as Marisa DeFranco.

At the convention in June, she attempted to turn Brown’s suggestion that she claimed Native American heritage to advance her teaching career from a demerit into a Democratic rallying point.

“I know what this fight is going to be about. I know how tough it’s going to be. I’ve gotten a taste of just how nasty it’s going to get,” she told attendees at a labor breakfast. “And you know what? I’m ready. So all I need to know is, are you ready?”

Warren has continued her pro-Democratic theme in her most recent campaign commercials, philosophical spots that have moved beyond the introductory bio pieces she first aired and are now fleshing out her policy beliefs.

One released last week focused on her plan to boost infrastructure spending.

“Our competitors are putting people to work, building a future,” she said. “China invests 9 percent of its GDP in infrastructure. America? We’re at just 2.4 percent. We can do better.”

In a statement accompanying the ad, the Warren campaign struck a partisan chord by saying, “Elizabeth’s plan is fully paid for by her debt and deficit reduction strategy, and ending special tax breaks for corporate jets, and ending public investment in the oil and gas research and development program.”

In a commercial released this week, Warren focuses on exploding student debt, saying, “America ought to be investing in education and building a future for our kids, but Washington’s giving billions to big oil and tax breaks to millionaires.”

By contrast, Brown has been trying to sell his bipartisan message with a series of ads featuring Democrats—albeit not necessarily political a-listers any more—who support his candidacy.

Critics have been quick to point out that some of the Brown backers, including former Boston Mayor Raymond L. Flynn and former Worcester Mayor Konnie Lukes, are social conservatives who have backed Republicans in the past.

But that complaint also overlooks what appear to be warning signs for Warren among even lifelong Democrats.

Former Senate President Tom Birmingham, whose hardscrabble rise from Chelsea to Harvard and a Rhodes scholarship is the stuff of liberal iconography, told the left-leaning New Republic for a story published last week: “I’m, candidly, perplexed by what’s going on. Because I did think that, if the Democrats had a strong candidate—and I would have regarded Elizabeth Warren as a strong candidate—that we’d really be in a favorable position.”

Jim Shannon, a former congressman and state attorney general, also was quoted in the same story as saying, “At this relatively late point in the campaign, I don’t have a fix on what type of candidate she is.”

Perhaps the biggest flare has been sent up by the current Boston mayor, Thomas M. Menino, who has conspicuously refused to endorse Warren.

The Democrat is the city’s longest-serving mayor and controls the Democratic apparatus in the state’s largest urban environment—the kind of voting bloc Democrats count on to offset the pro-Republican electorate that typically resides in the suburbs.

Last September, when it was clear Warren planned to get into the race, Menino nonetheless praised Brown’s work ethic and told the Globe that the senator “has something about him that people gravitate to.”

While Menino chastised Brown for his focus on Warren’s claim of Native American heritage, he expressly refused to back her even after she claimed 96 percent of the vote at the Democratic State Convention in June.

Nonetheless, the Warren campaign and state Democrats continue to take comfort in numbers.

Warren has outraised Brown throughout this year, and emerged as the top fund-raiser among all congressional candidates in the country.

She has virtually erased Brown’s cash advantage, with a campaign kitty of $13.5 million in her most recent report, compared with $15.5 million for Brown.

Both have started spending that money on the TV ads reaching out to their different target audiences.

Polls have also shown a majority of voters were not affected by the Native American flap, and that Warren has been ahead of or tied with Brown. That is an accomplishment, considering she is a first-time political candidate and he is a veteran campaigner and sitting US senator.

The candidates’ schedules also bear out their differing approaches to a campaign now mirroring the welfare focus in the presidential race.

Brown’s is replete with triathlons and diner stops, aimed at perpetuating the everyman image he believes can draw votes from not just Republicans but Democrats, as well as that majority of unenrolled voters.

Warren, too, visited an ice cream social last weekend, a diner last week, and the Lowell Folk Festival and Boston Puerto Rican Festival two weeks ago.

But she has also spent a lot of time ensuring the Democratic base turns out for her this fall.

On Wednesday, her only public appearances were at three “Women for Warren” phone banks—including one staged from a Quincy union office.